Vol. 5, Issue 4, Part E (2019)

It was Koshy (2010) who introduced and investigated the concept Complementary Distance Pattern Uniform (CDPU) sets in a connected graph. In this paper, the researcher introduces one variety of Complementary Distance Pattern Uniform (CDPU) graphs which is α Complementary Distance Pattern Uniform (αcdpu) graphs.

A couple of results are generated in this study. Some of which are the following: α(G + H) ≤ min {|V(G)|,|V(H)|} where G and H be connected graphs. Let G be a connected graph and H be a disconnected graph. Then α (G + H) ≤ |V(G)|. Let G be a self-centered graph and H be any graph. Then α (G â—¦ H) = |V(G)|. Let Knbe a complete graph of order n and H be any graph. Then α (Knâ—¦ H) = n. Let Cn be a cycle of order n and H be any graph. Then α (Cnâ—¦H)=n. Let G and H be graphs with isolated vertices u ϵ V(G) and v ϵ V(H). Then αu (G+H) = 2. Let K1,n, and Km,nbe a star of order n +1 and a complete bipartite graph of order n + m, respectively.